The best time to launch is just about NOW
Would you really be willing to wait for, say half a year if you concluded that that would be the best time of year to launch? I would suggest that you launch as soon as you are ready.
I could imagine some reasons to wait with launching. This could be to get a critical mass of users who are online at the same time. This could be essential for launching something like a chat service. Do you have any such reasons?
Don't launch during peak season for the restaurant industry if there is ANY chance that glitches or a failure of your technology could cause problems in their business or stop them from serving customers and capitalising on their busy times. They will hate you for it and you will lose customers for life. Much better to launch at a quieter time where you have more time and tolerance to work out any problems that might occur.
Of course, you should launch sooner rather than later, but if it was near a peak season (like Christmas or Thanksgiving for example) I would wait till that was over.
It doesn't matter, at all. Why should it?